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Mathematical Problems in Engineering
Volume 2014, Article ID 273732, 9 pages
Research Article

An Efficient Approach for Solving Mesh Optimization Problems Using Newton’s Method

Department of Computer Science and Engineering, Incheon National University, Incheon 406-772, Republic of Korea

Received 22 May 2014; Revised 12 September 2014; Accepted 6 October 2014; Published 21 October 2014

Academic Editor: Tiedong Ma

Copyright © 2014 Jibum Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present an efficient approach for solving various mesh optimization problems. Our approach is based on Newton’s method, which uses both first-order (gradient) and second-order (Hessian) derivatives of the nonlinear objective function. The volume and surface mesh optimization algorithms are developed such that mesh validity and surface constraints are satisfied. We also propose several Hessian modification methods when the Hessian matrix is not positive definite. We demonstrate our approach by comparing our method with nonlinear conjugate gradient and steepest descent methods in terms of both efficiency and mesh quality.